Theorem simp3i 1142

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089

This theorem is referenced by:  hartogslem2  9458  harwdom  9506  divalglem6  16367  structfn  17126  strleun  17127  oppchomfval  17680  sratset  21178  srads  21180  tngip  24612  dfrelog  26529  log2ub  26913  birthdaylem3  26917  birthday  26918  divsqrtsum2  26946  harmonicbnd2  26968  lgslem4  27263  lgscllem  27267  lgsdir2lem2  27289  lgsdir2lem3  27290  mulog2sumlem1  27497  siilem2  30923  h2hva  31045  h2hsm  31046  h2hnm  31047  elunop2  32084  wallispilem3  46495  wallispilem4  46496  prstchomval  50034  cnelsubclem  50078